Embedding and compact embedding of weighted Bergman spaces

Source abstract

We use embeddings of Bergman spaces and fractional radial differential operators to study the Lαp–Lβq mapping properties of Bergman-type projections on the open unit ball of Cn. We recover and extend several existing results in this direction. In particular, this approach allows us to treat the cases when 0<q<1 and α≤−1. We also characterize when the embedding of one weighted Bergman space into another is compact.